# Approximated TSP: weight of minimum spanning tree less than cost of the optimal tour?

In the chapter, Approximation Algorithms of Introduction to Algorithm, 3rd Edition, for the approximation problem Travelling Salesman Problem, the author proposes a approximation method that first constructs a minimum spanning tree.

In order to prove this algorithm is a 2-approximation algorithm, the author claims that:

The weight of the minimum spanning tree $T$ is less than the cost of the optimal tour.

I am wondering if the minimum spanning tree(which is acyclic) of $G$ ensures that its weight is necessarily smaller than any tour(which is cyclic) of the same graph $G$

PS:

The original claim is: